AdS/CFT correspondence with a three-dimensional black hole simulator

Abstract

One of the key applications of AdS/CFT correspondence is the duality it dictates between the entanglement entropy of anti–de Sitter (AdS) black holes and lower-dimensional conformal field theories (CFTs). Here we employ a square lattice of fermions with inhomogeneous tunneling couplings that simulate the effect rotationally symmetric three-dimensional (3D) black holes have on Dirac fields. When applied to 3D Banados-Teitelboim-Zanelli (BTZ) black holes we identify the parametric regime where the theoretically predicted two-dimensional CFT faithfully describes the black hole entanglement entropy. With the help of the universal simulator, we further demonstrate that a large family of 3D black holes exhibit the same ground-state entanglement entropy behavior as the BTZ black hole. The simplicity of our simulator enables direct numerical investigation of a wide variety of 3D black holes and the possibility to experimentally realize it with optical lattice technology

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